This morning my dog Walter broke out of the house and ran di

This morning, my dog Walter broke out of the house and ran directly to the farm up the road at a speed of 12mph. When he arrived at the farm he was scared by the cows so he turned around and ran directly home (by the same route) at a speed of 8mph. Walter spent a total time of one hour running to the farm and back. Find the distance from my house to the farm.

Solution

Let t = time to get to the farm
then
1-t = time to get back to the house
.
Applying the distance formula:
d = rt
where
d is distance
r is rate or speed
t is time
.
12t = 8(1-t)
12t = 8-8t
20t = 8
t = 8/20
t = 2/5 hour (to run from house to farm)
.
Distance then is:
d = (2/5)12
d = 24/5 = 4.8 miles (distance from house to farm)